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Algebra
Question

Given a degree \( 4 \) polynomial \( g ( x ) \) wi...

Given a degree \( 4 \) polynomial \( g ( x ) \) with real coefficients that has the leading coefficient \( 2 \) , and has the zeros \( 3 i , - 4 \) and \( 5 \) . 

(a) ( \( 5 \) points) Find the complete factored form of \( g ( x ) \) . That is, write \( g ( x ) \) as a product of linear factors. 

(b) \( ( 5 \) points) Expand \( g ( x ) \) into polynomial form 

\( g ( x ) = a _ { n } x ^ { n } + a _ { n - 1 } x ^ { n - 1 } + \cdots + a _ { 2 } x ^ { 2 } + a _ { 1 } x + a _ { 0 } \) . 

Answer

Solution
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